Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9001	(2^223754+658)/2	67357	Stefano Morozzi	01/2020
9002	V(340138)	67336	Serge Batalov	03/2015
9003	43125^14528-106	67334	Enzo Doria	07/2012
9004	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
9005	8*10^67302-51	67303	Robert Price	10/2017
9006	(2^223551+1634)/2	67296	Stefano Morozzi	01/2020
9007	17458^7153+7153^17458	67292	Hans Havermann	08/2016
9008	16366^12925+12925^16366	67288	Hans Havermann	08/2016
9009	37^42906-2	67286	Lelio R Paula	08/2013
9010	18^53592-13	67273	Lelio R Paula	08/2013
9011	V(396221)	67256	Serge Batalov	03/2015
9012	(2^223401+906)/2	67251	Stefano Morozzi	01/2020
9013	(2^223382+2338)/2	67245	Stefano Morozzi	01/2020
9014	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
9015	(14*10^67235-101)/3	67236	Robert Price	04/2017
9016	53^38993-52^38993	67235	Robert Price	01/2013
9017	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
9018	2^223333+315	67230	Lelio R Paula	04/2012
9019	(2^223318+574)/2	67226	Stefano Morozzi	01/2020
9020	(2^223301+1590)/2	67220	Stefano Morozzi	01/2020
9021	2^223278-111041	67214	Enzo Doria	05/2014
9022	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
9023	2^223256-45	67207	Lelio R Paula	02/2012
9024	2^223253-112111	67206	Enzo Doria	06/2014
9026	18407^4474+4474^18407	67199	Hans Havermann	08/2016
9025	(2^223228+3342)/2	67199	Stefano Morozzi	01/2020
9027	(2^223206+2194)/2	67192	Stefano Morozzi	01/2020
9028	47^40182+40182^47	67189	Norbert Schneider	11/2014
9029	13^60309+94	67181	Lelio R Paula	07/2013
9030	11^64503-84	67173	Lelio R Paula	07/2013
9031	3^140781+236	67170	Lelio R Paula	06/2013
9032	(2^223110+3382)/2	67163	Stefano Morozzi	01/2020
9033	2^223107-865057	67162	Paul Bourdelais	03/2013
9034	2^223100-59	67160	Lelio R Paula	02/2012
9035	(2^223098+2394)/2	67159	Stefano Morozzi	01/2020
9036	2^223087+71963	67156	Enzo Doria	04/2016
9037	(2^223032+2410)/2	67140	Stefano Morozzi	01/2020
9038	(2^223034+1122)/2	67140	Stefano Morozzi	01/2020
9040	18^53481-3779	67134	Enzo Doria	03/2013
9039	(326^26713-1)/325	67134	Eric Chen	09/2017
9041	4^111473-62573	67114	Mike Oakes	02/2011
9042	2^222943+29	67113	Henri Lifchitz	08/2005
9043	(2^222939-9)/103	67110	Lelio R Paula	04/2012
9044	2^222862-459161	67089	Enzo Doria	05/2015
9045	2^222828+8193	67078	Lelio R Paula	04/2012
9046	3^140570+2660	67069	Lelio R Paula	06/2013
9047	20731^1716+1716^20731	67055	Hans Havermann	08/2019
9048	2^222744+855	67053	Lelio R Paula	04/2012
9049	13^60189+84	67048	Lelio R Paula	07/2013
9050	(2^222721+2034)/2	67046	Stefano Morozzi	01/2020
9051	2*10^67043-51	67044	Robert Price	11/2017
9052	22588^929+929^22588	67042	Hans Havermann	08/2019
9053	2^222701+577294575	67040	Lelio R Paula	02/2016
9054	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
9055	(151*10^67027-7)/9	67029	Robert Price	07/2017
9056	(2^222659+1554)/2	67027	Stefano Morozzi	01/2020
9057	(2^222640+3810)/2	67022	Stefano Morozzi	01/2020
9058	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
9059	2^222614-111041	67014	Enzo Doria	05/2014
9060	16255^13242+13242^16255	67003	Hans Havermann	08/2019
9061	16477^11650+11650^16477	67001	Hans Havermann	08/2019
9062	118^32333-117	66991	Norbert Schneider	08/2018
9063	2^222520-1907	66986	Yves Minet	03/2013
9064	(2^222499+2694)/2	66979	Stefano Morozzi	01/2020
9065	(4^111231+23)/3	66968	Robert Price	02/2017
9066	16206^13549+13549^16206	66962	Hans Havermann	08/2019
9067	2^222408-111275	66952	Enzo Doria	05/2014
9068	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
9069	(2^222394+2790)/2	66947	Stefano Morozzi	01/2020
9070	2^222378-1005	66943	Lelio R Paula	04/2012
9071	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
9072	7^79202-6^(79202+1)	66934	Robert Price	06/2016
9073	2^222325-112255	66927	Enzo Doria	06/2014
9074	(2^222318+1290)/2	66925	Stefano Morozzi	01/2020
9075	21789^1178+1178^21789	66918	Hans Havermann	08/2019
9076	20^51428+33	66910	Lelio R Paula	08/2013
9077	(2^222237+2682)/2	66900	Stefano Morozzi	01/2020
9079	2^222224-18509	66897	Enzo Doria	05/2013
9078	(38*10^66896+187)/9	66897	Robert Price	11/2017
9080	(2^222205+1826)/2	66891	Stefano Morozzi	01/2020
9081	2^222192-869688105	66887	Lelio R Paula	02/2016
9082	(2^222175+3206)/2	66882	Stefano Morozzi	01/2020
9083	(19*10^66878-43)/3	66879	Robert Price	10/2017
9084	11^64219-64	66878	Lelio R Paula	07/2013
9085	2^222151-17295	66875	Lelio R Paula	04/2012
9086	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
9087	2^222085-111031	66855	Enzo Doria	05/2014
9088	8*10^66848-13	66849	Robert Price	05/2017
9089	(3^140087+4)/13	66838	Lelio R Paula	04/2012
9090	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
9091	19^52265+52	66835	Lelio R Paula	08/2013
9092	2*10^66826-27	66827	Robert Price	02/2017
9093	(2^221971+3686)/2	66820	Stefano Morozzi	01/2020
9094	4*6^85867+5	66819	Lelio R Paula	09/2014
9095	11955^16384+2	66807	Matt Stath	12/2018
9096	15^56800+8	66802	Lelio R Paula	08/2013
9097	(2^221891-2^110946+1)/5	66796		11/2006
9098	10^66793+69441	66794	Patrick De Geest	05/2013
9099	10^66793-63	66793	Robert Price	05/2011
9100	(2^221880+2730)/2	66793	Stefano Morozzi	01/2020
9101	35^43256-1704	66791	Enzo Doria	03/2013
9102	3^139976+2^(139976-1)	66786	Robert Price	05/2016
9103	88769!6-48	66786	Robert Price	08/2018
9104	7^79023-54	66783	Lelio R Paula	06/2013
9105	104^33109-103	66782	Norbert Schneider	11/2016
9106	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
9107	(2^221812+1290)/2	66772	Stefano Morozzi	01/2020
9108	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
9110	2^221768+183	66759	Lelio R Paula	02/2012
9109	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
9111	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
9112	11^64097+48	66751	Lelio R Paula	07/2013
9113	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
9114	(19*10^66748+413)/9	66749	Robert Price	10/2017
9115	(2^221732+2490)/2	66748	Stefano Morozzi	01/2020
9116	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
9117	8*6^85758-7	66734	Lelio R Paula	09/2014
9119	135^31325+2	66733	Lelio R Paula	05/2013
9118	(2^221682+3750)/2	66733	Stefano Morozzi	01/2020
9120	(49*10^66729+41)/9	66730	Robert Price	07/2015
9121	(2^221650+430)/2	66723	Stefano Morozzi	01/2020
9122	(349*10^66720-7)/9	66722	Robert Price	03/2017
9123	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
9124	(2^221624+2170)/2	66716	Stefano Morozzi	01/2020
9125	(25*10^66714+71)/3	66715	Robert Price	01/2017
9126	11^64061-780	66713	Enzo Doria	11/2012
9127	(2^221590+3238)/2	66705	Stefano Morozzi	01/2020
9128	7^78929+4	66703	Lelio R Paula	06/2013
9129	11^64048-930	66700	Enzo Doria	11/2012
9131	120^32079-119	66699	Norbert Schneider	09/2018
9130	(2^221567+1418)/2	66699	Stefano Morozzi	01/2020
9132	2*7^78921+5	66697	Lelio R Paula	09/2014
9133	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
9134	16330^12117+12117^16330	66682	Hans Havermann	08/2019
9136	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
9135	(2^221483+1218)/2	66673	Stefano Morozzi	01/2020
9137	2^221479+72953	66672	Enzo Doria	04/2016
9139	10^66666+275403	66667	Patrick De Geest	03/2010
9138	16317^12182+12182^16317	66667	Hans Havermann	08/2019
9140	10^66666-115521	66666	Patrick De Geest	03/2010
9141	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
9142	(2^221425+1746)/2	66656	Stefano Morozzi	01/2020
9143	4*10^66653+21	66654	Robert Price	08/2016
9144	(10^66650+149)/3	66650	Serge Batalov	12/2014
9145	(2^221398+3654)/2	66648	Stefano Morozzi	01/2020
9146	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
9147	2^221391-2145	66646	Lelio R Paula	04/2012
9148	22952^801+801^22952	66645	Hans Havermann	08/2019
9149	(2^221347+3146)/2	66632	Stefano Morozzi	01/2020
9150	(5*10^66613-119)/3	66614	Robert Price	04/2016
9151	2^221273-113233	66610	Enzo Doria	07/2014
9152	(2^221234+2994)/2	66598	Stefano Morozzi	01/2020
9153	3^139571-46	66593	Lelio R Paula	06/2013
9154	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
9155	2^221181-869688105	66583	Lelio R Paula	02/2016
9156	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
9157	(2^221131+1850)/2	66567	Stefano Morozzi	01/2020
9158	2^221126+133	66566	Lelio R Paula	02/2012
9159	12^61680+91	66564	Lelio R Paula	07/2013
9160	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
9161	(2^221090+1782)/2	66555	Stefano Morozzi	01/2020
9162	(13*10^66551-73)/3	66552	Robert Price	12/2016
9163	11^63901-1590	66547	Enzo Doria	12/2012
9164	11^63901-1500	66547	Enzo Doria	12/2012
9165	6^85517+23	66546	Lelio R Paula	07/2013
9166	(2^221047+566)/2	66542	Stefano Morozzi	01/2020
9169	17^54069-40	66530	Lelio R Paula	08/2013
9167	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
9168	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
9170	(2^221004+450)/2	66529	Stefano Morozzi	01/2020
9172	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
9171	3^139432+26	66526	Lelio R Paula	06/2013
9173	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
9174	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
9175	6^85481+85481	66518	Henri Lifchitz	08/2014
9176	(2^220925+3834)/2	66505	Stefano Morozzi	01/2020
9177	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
9178	13^59687+66	66488	Lelio R Paula	07/2013
9179	(49*10^66485-31)/9	66486	Robert Price	07/2015
9180	(2^220841+1062)/2	66480	Stefano Morozzi	01/2020
9181	(2^220815+950)/2	66472	Stefano Morozzi	01/2020
9182	(46*10^66469+17)/9	66470	Robert Price	06/2015
9183	2^220790+97	66465	Lelio R Paula	02/2012
9184	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
9185	40009^14441-102	66460	Enzo Doria	07/2012
9186	(2^220766+3190)/2	66457	Stefano Morozzi	01/2020
9187	2^220736-143	66449	Lelio R Paula	02/2012
9188	61077!4-64	66448	Robert Price	11/2019
9189	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
9190	21235^1344+1344^21235	66432	Hans Havermann	08/2019
9191	2^220675+69	66430	Lelio R Paula	02/2012
9192	(2^220671+498)/2	66429	Stefano Morozzi	01/2020
9194	19049^3070+3070^19049	66427	Hans Havermann	08/2019
9193	(2^220665+974)/2	66427	Stefano Morozzi	01/2020
9196	88323!6-16	66419	Robert Price	08/2018
9195	(2^220637+3974)/2	66419	Stefano Morozzi	01/2020
9197	2^220633-111381	66418	Enzo Doria	05/2014
9198	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
9199	2^220596-15813	66407	Enzo Doria	04/2013
9200	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
9201	2^220549-1859173	66392	Enzo Doria	04/2016
9202	(2^220519+3858)/2	66383	Stefano Morozzi	01/2020
9203	(2^220514+1294)/2	66382	Stefano Morozzi	01/2020
9204	(2^220485+3434)/2	66373	Stefano Morozzi	01/2020
9205	2^220478-161	66371	Lelio R Paula	02/2012
9206	(2^220470+1278)/2	66368	Stefano Morozzi	01/2020
9207	5^94938-14636	66359	Enzo Doria	02/2013
9208	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
9209	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
9210	2^220253-114871	66303	Enzo Doria	05/2015
9211	(2^220244+3226)/2	66300	Stefano Morozzi	01/2020
9212	12^61432+95	66297	Lelio R Paula	07/2013
9213	2^220192-111563	66285	Enzo Doria	05/2014
9214	2^220188-111449	66284	Enzo Doria	05/2014
9215	(4*10^66284+23)/9	66284	Robert Price	11/2014
9216	(2^220155+1626)/2	66273	Stefano Morozzi	01/2020
9217	(2^220150+2950)/2	66272	Stefano Morozzi	01/2020
9218	32501!2+2	66266	Robert Price	01/2015
9219	(8*10^66261-101)/3	66262	Robert Price	10/2017
9220	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
9221	(47^39623-1)/46	66252	Robert Price	06/2014
9222	(2^220081+794)/2	66251	Stefano Morozzi	01/2020
9223	2^220044-97305	66240	Lelio R Paula	04/2012
9224	(77*10^66237-257)/9	66238	Robert Price	10/2017
9226	29^45285+2	66225	Ray Chandler	08/2011
9225	(2^219993+1754)/2	66225	Stefano Morozzi	12/2019
9227	16711^9178+9178^16711	66222	Hans Havermann	08/2019
9228	(2^219928+462)/2	66205	Stefano Morozzi	12/2019
9229	15^56289+38	66202	Lelio R Paula	08/2013
9230	3^138749+98	66201	Lelio R Paula	06/2013
9231	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
9233	2^219904-16995	66198	Lelio R Paula	10/2011
9232	2^219903-4615	66198	Yves Minet	05/2019
9234	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
9235	Phi(198552,10)	66177	Ray Chandler	07/2010
9236	4*6^85041+7	66176	Lelio R Paula	09/2014
9237	16777^8794+8794^16777	66172	Hans Havermann	08/2019
9238	2^219812-3149	66171	Yves Minet	10/2009
9239	2^219795-611167	66165	Paul Bourdelais	03/2013
9240	32455!2+512	66162	Robert Price	02/2015
9241	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
9243	(11^63521-4^63521)/7	66150	Robert Price	03/2013
9242	5*7^78274-6	66150	Lelio R Paula	09/2014
9244	15853^14872+14872^15853	66145	Hans Havermann	08/2019
9245	(2^219706+1282)/2	66138	Stefano Morozzi	12/2019
9246	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
9247	2^219679-112015	66130	Enzo Doria	05/2014
9248	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
9249	(2^219621+2670)/2	66113	Stefano Morozzi	12/2019
9250	15445^15782-15782^15445	66108	Norbert Schneider	08/2018

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